Let ABC be a triangle with AB = 2, BC = 5, AC = 4. Let M be the projection of C onto the external angle bisector at vertex B. Similarly, let N be the projection of B onto the external angle bisector at vertex C. If the ratio of the area of quadrilateral BCNM to the area of \triangle ABC is \frac{a}{b}, where a and b are positive integers and \gcd(a, b) = 1, find a + b.